1. ## Compact Sets

Let S be a subset of the reals. Prove that S is compact iff every infinite subset of S has an accumulation point in S.

This is what I have so far (which is not much):
Let S be compact
Then every infinite subset of S has an accumulation point in S by Bolzano Weierstrass.

Going the other way is giving me troubles, so any help on that would be much appreciated.

2. Originally Posted by steph615
Going the other way is giving me troubles, so any help on that would be much appreciated.
Hint: A set is closed if and only if every every convergent sequence in S has its limit in S.